Monte-Carlo simulations of the clean and disordered contact process in three dimensions

TL;DR

This study uses Monte-Carlo simulations to analyze the critical behavior of the three-dimensional contact process with and without quenched disorder, revealing universal infinite-randomness critical points and Griffiths phases.

Contribution

It provides high-precision characterization of the critical behavior in both clean and disordered three-dimensional contact processes, highlighting the universality of the infinite-randomness critical point.

Findings

Clean case follows three-dimensional directed percolation universality class.

Disordered case exhibits an infinite-randomness critical point with activated scaling.

Presence of Griffiths phase with nonuniversal power laws.

Abstract

The absorbing-state transition in the three-dimensional contact process with and without quenched randomness is investigated by means of Monte-Carlo simulations. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. In the presence of quenched spatial disorder, our data demonstrate that the absorbing-state transition is governed by an unconventional infinite-randomness critical point featuring activated dynamical scaling. The critical behavior of this transition does not depend on the disorder strength, i.e., it is universal. Close to the disordered critical point, the dynamics is characterized by the nonuniversal power laws typical of a Griffiths phase. We compare our findings to the results of other numerical methods, and we relate them to a general classification of phase transitions in disordered systems based on the rare region dimensionality.